Step-by-step explanation:
A (-2,1) B (3,4) find the gradient of the line
m = -1
we know that=
m/y2 - y 1) / (x2-1)
= (-4-1)/{3-(-2)
=-5/(3+2)
=5/5
= 1
If tan 0 = 4/3 and 0 lies in the third quadrant, which is the correct ratio for cos 0?
4/5
-3/5
-4/5
3/5
[tex] \frac{ - 3}{5} \\ [/tex]
because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.
then ,
[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]
hope helpful.
The answer is cos 0 = -3/5
To calculate the answer:Given :
tan 0 = 4/3 and is in the 3rd quadrant
this implies that both the perpendicular and base are negative.
Perpendicular = -4
Base = -3
Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{25} = 5[/tex]
cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]
cos 0 = -3/5
Therefore, cos 0 = -3/5
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7% tax on a $3 soda with an $8 burger
Step-by-step explanation:
please mark me as brainlest
Which formula can be used to describe the sequence? f(x) = 1.2(2.5)x – 1 f(x) = 2.5(1.2)x – 1 f(x) = 1.2(2.5)x f(x) = 2.5(1.2)x
The formula which used to describe the sequence is f(x)=1.2(2.5)ˣ⁻¹.
The given sequence is 1.2,3,7.5,18.75.
In geometric series, the ratio of two consecutive terms remains the same and this ratio is known as common ratio. a₁ is the first term of a geometric sequence and r is the common ratio, then the general term of the geometric sequence is of the form:
f(x)=a₁⋅rˣ⁻¹.
In the given sequence, a₁=1.2, a₂=3, a₃=7.5 and a₄=18.75.
Find the common ratio by
r=(aₙ₊₁)÷aₙ
r=a₂÷a₁
r=3÷1.2
r=2.5
Substitute the values in the general formula of geometric sequence.
f(x)=(1.2)(2.5)ˣ⁻¹
Hence, the formula which used to describe the sequence 1.2,3,7.5,18.75 is f(x)=(1.2)(2.5)ˣ⁻¹.
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Five hundred ten of 650 high school students said that pizza was their favorite food in the school cafeteria.
what is the margin of error? round to four decimal places.
0.0005
0.0003
0.0161
0.0322
If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.
Margin of errorGiven:
Sample proportion=Five hundred ten=510
Sample size=650
Hence:
Margin of error=z×√p×(1-p)/n
Margin of error=2√510/650× (1-510/650)÷650
Margin of error=2√0.78461538×(1-0.78461538)÷650
Margin of error=2√0.78461538×0.21538462÷650
Margin of error=2√0.168994085÷650
Margin of error=2√0.0002599909
Margin of error=0.0322
Therefore the correct option is D.
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What is the measure of the central angle of a circle with radius 60 cm the intercepts a 15 pi centimeters arc
The measure of the central angle of a circle is 45⁰
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Here,
Theta (angle) θ = arc length / radius
θ = 15 π / 60 cm
θ = 0.79 radians
Convert to degrees
θ = 0.79 radians = 0.79 X 180/ π
= 0.79 X 180/ 3.14
= 45⁰
Thus, the measure of the central angle of a circle is 45⁰.
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help me
A rectangle has a length of 10.3 centimeters and a width of 6.8 centimeters.
What is the area of this rectangle?
34.2 cm²
35.02 cm²
70.04 cm²
108.24 cm²
Answer:
70.04 cm²
Step-by-step explanation:
Area = base x height
10.3 x 6.8 = 70.04
Hope this helps :)
Does anyone know the answer
Answer: two units to the left, four units down and reflected across the y axis
Determine the intervals on which the function is (a) increasing; (b) decreasing: (c) constant.
(a) The function is increasing on the interval(s)
(Use a comma to separate answers as needed. Type your answer in interval notation.)
The intervals of the function in which it is increasing, decreasing and constant are given as follows:
a) Increasing: [tex]x \in \left[-4.5, 2\right][/tex].
b) Decreasing: [tex]x \in \left[4,6\right][/tex].
c) Constant: [tex]x \in \left[2,4\right][/tex].
When a function is increasing?A function is increasing when the graph of the function is pointing upwards, hence this function is increasing on the interval [tex]x \in \left[-4.5, 2\right][/tex].
When a function is decreasing?A function is increasing when the graph of the function is pointing downwards, hence this function is decreasing on the interval [tex]x \in \left[4, 6\right][/tex].
When a function is constant?A function is constant when it is graph is a line without inclination, hence this function is constant n the interval [tex]x \in \left[2, 4\right][/tex].
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If x² + 1/x² = 102, then x -1/x =
a) 10
b) 8
c) 13
d) 12
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]
[ subtract 2 from both sides ]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]
[ 2 can written like that, as they cancel out each other ]
Apply Identity [ a² + b² -2ab = (a - b)² ]
[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A computer system is priced at $3200. A man buys
the computer system on hire purchase according
to the following terms: a down payment of $480
and the remaining to be paid in monthly
instalments over 2 years at a simple interest rate of
9.5% per annum.
(i) Find his monthly instalment.
(ii) Find the total amount the man pays for the
computer system.
(iii) How much more does he have to pay
for
buying the computer system on hire purchase?
dollar
(i) Monthly installment is $21.53 approximately.
(ii) Total amount man has to pay is $3716.8
(iii) Extra money he had to pay for buying the computer on hire is $516.8
Given,
Initial price of the computer(p) = $3200
Down payment = $480
Time period = 2 yrs
rate percent = 9.5%
(i) Monthly installment = ?
monthly installment =(capital amount × interest rate)/time in months
down payment to be paid = 3200 ₋ 480
= 2720
therefore, monthly payment = 2720 × 9.5 × 1/ 12
= $21.53
(ii) Total amount man has to pay = ?
= down payment ₊ remaining amount ₊ (remaining amount × t × r)
= 480 ₊ 2720 ₊ 2720 × 9.5 × 2
= $3716.8
(iii) If he buys the computer on hire then how much more he has to pay = ?
= total amount ₋ initial cost
= 3716.8 ₋ 3200
= $516.8
Hence the man has to pay $21.23 as a monthly installment, $3716.8 as a total cost of the computer system and $516.8 as an extra amount if he buys it on hire.
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I’ve been stuck in this for almost 20 minutes
help :/
Answer:
pi/2 units to the left
Step-by-step explanation:
the formula is y = cos(x-b) so when b is negative, the formula will show a plus sign because minus negative is adding. this means the graph is shifted -pi/2 to the right which is really pi/2 to the left
state whether or not the relation is considered a function?
Answer:
A function is when each input has exactly one output
Step-by-step explanation:
Each input can only have one output, but an output can have multiple inputs.
J
Question 1 of 10
Each equation given below describes a parabola. Which statement best
compares their graphs?
x = 5y²
x=3y²
OA. Both parabolas open upward, and x = 3y2 is wider than
x = 5y².
B. Both parabolas open to the right, and x = 3y² is wider than x = 5y².
OC. Both parabolas open upward, and x = 5y2 is wider than
x = 3².
OD. Both parabolas open to the right, and x = 5y² is wider than x = 3y².
SUBMIT
Answer:
D
Step-by-step explanation:
x = 5y²
x = 3y²
Here x is a function of y and so the parabola is open either to right or left.
The coefficient of y² is positive. So the parabola is open to right.
Both parabolas are open to right and x = 5y² is wider than x = 3y².
Prove: 45= m/ZXY
Complete the proof. Number your reasons in the textbox below.
Step-by-step explanation:
since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful
What is the degree of 069 ?
A. 0
B. 2
C. 3
D. 4
E. none of these
Answer: none
Step-by-step explanation:
The perimeter of a triangle is 84 cm and it's area is 336cm².If one of it's sides is 30 cm find the length of other two sides.
Answer:
26,28
Step-by-step explanation:
We can make a system of equations based on the information given
first we can make one for the perimeter
and one for the area using herons formula
(x and y are the two unknown sides)
[tex]84=30+x+y[/tex]
[tex]336=\sqrt{42(12)(42-x)(42-y)}[/tex]
Now solve for x and y or you can find it by graphing
x and y = 26 and 28, the order does not matter since they are both unkown
so the two sides are 26 and 28
Charlie owns a computer repair service. For each computer, they charge $50 plus $45 per hour of work. A linear equation that expresses the total amount of money Charlie earns per computer is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope?
Answer:
The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.
y-intercept: (0,50)
Slope: 45
ayuda porfaaa JHAKJAH es para hoy y no entiendo un klo
A) Hala los números que hagan verdadera la adición.
a) +2 + ? = 29
b) ? + (-13) = -17
c) -17 + ? = -38
d) ? + (25) = 13
e) ? + 12 = -2
B) Encuentra el resultado de las siguientes adiciones.
a) +5 + (-12) =
b) -10 + (-13) =
c) 20 + (-17) =
d) -80 + 10 =
e) 40 + (-60) =
vence hoy:(
Hurry pleaeeeee show your work
117n + 90=
Answer:
n=-0.769
Step-by-step explanation:
Since there is no number after the equal sign in the equation given, we can put a zero in that place.
117n+90=0
Subtract 90 from both sides.
117n=-90
Divide 117 and -90
n=-0.769
Hope this helps!
If not, I am sorry.
Todd is 3 years older than his brother Jack. If Jack is x years old and Todd is y years old, write a rule that relates their ages over time. When Jack is 28 years old, how old will Todd be?
A rule that relates their ages over time is given by y = x+3 , When Jack is 28 years , Todd will be 31 years old.
What are Variables ?Variables are generally alphabets that are used to denote the unknown values in any process or equation.
If Jack is x years old
Todd is y years old
Todd is 3 years older than his brother Jack.
a rule that relates their ages over time is given by
y = x+3
When Jack is 28 years old
Todd will be
y = 28+3
y = 31 years
Therefore Todd will be 31 years old.
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Is this correct? If not then whats the answer?????
(image below)
Answer:
6
Step-by-step explanation:
Mean no. of runs per game =
= Total no. of runs/ total no. of games
= 9+8+4+0+7+6+4+5+9+8 / 10
= 60 / 10
= 6
It’s 12 points if you help me thank you :)
Based on the calculations, Celine would earn a total of $65.00 assuming she delivered 10 packages.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variable.
Given the following function:
y = 20.00 + 0.45(x)
In this exercise, you're required to determine Celine's weekly earnings based on the number of packages she delivered. However, the number of packages delivered by Celine wasn't shown, thus, we would assume a value for the purpose of an explanation:
Assuming x = 10 packages.
Substituting the value of x into the function, we have:
y = 20.00 + 0.45(10)
y = 20.00 + 45
y = $65.00.
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Is this correct?? If not then whats the answer.
(image below)
Brainly for the first person to answer
this question
Answer:
fair share
Step-by-step explanation:
all are equal.
Find the range for the given domain: {-2, -1, and 0} and the function is y = 3x2.
The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
What is range?
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that:-
The range for the given domain: {-2, -1, and 0} and the function is y = 3x².
The range will be the value of y at each given value of the domain.
Domain: { -2, -1, 0 }
y = 3x²
At x = -2 → y = 3 ( -2)² = 12
At x = -1 → y = 3 (-1)² = 3
At x = 0 → y = 3 (0) = 0
Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
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Randy and trey take turns cleaning offices on the weekends. it takes randy at most 4 hours to clean the offices. it takes trey at most 6 hours to clean the offices. what is the greatest amount of time it would take them to clean the offices together?
Answer:
2.4 hours
Step-by-step explanation:
Because 1 hour Randy clean 1/4 of the room and Trey is 1/6. So we add both together and get that they clean 5/12 of the office in one hour. So 2.4 hours is the greatest amount of time it would take them to clean offices together
1. (08.01 MC)
The graph shows two lines. A and B
Answer:
Part A:
A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.
Part B:
The solution would be (3, 4) because it is the point of intersection between the two linear lines.
Solve equation
-15+n=-9
A swimming pool of 25m long and 20m wide is filled with water to a depth of 5m. what is the volume of water when it is 3/4 full?
Answer:
[tex]1875m^{3}[/tex]
Step-by-step explanation:
To find [tex]\frac{3}{4}[/tex] of the volume, we first must know the total volume.
The formula to find volume:
[tex]volume = length * width * depth[/tex]
We know the length is 25m, we know the width is 20m and we know the depth is 5m.
So, we can substitute them into the equation:
[tex]volume=25*20*5=2500m^{3}[/tex]
Now we know the total volume, we can find out the volume when it is [tex]\frac{3}{4}[/tex] full:
[tex]\frac{3}{4} * 2500 = 1875m^3[/tex]
Therefore, our final answer is [tex]1875m^{3}[/tex].
Ving tools to form the correct answer on the graph.
Graph the line that represents this equation:
y + 2 =
(x+2)
Drawing Tools
Select
Point
Line
Click on a tool to begin drawing.
10
N
27
The graph of the equation is shown in the attached picture which is a straight line.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a graph of a equation:
y + 2 = (x+2)
or
y = x
The above equation is a linear equation or straight line equation the slope of the equation is 1.
m = 1
The y-intercept of the equation is 0.
We can plot the equation y = x by using the slope and y-intercept.
Thus, the graph of the equation is shown in the attached picture which is a straight line.
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Find the coordinates of the intersection of the diagonals of parallelogram HJKL with the given vertices: H(-1, 4), J(3, 3), K(3, -2), L(-1, -1). (Drawing a picture helps!)
thank you!
Answer:
(1, 1)
Step-by-step explanation:
Given vertices of the parallelogram:
H = (-1, 4)J = (3, 3)K = (3, -2)L = (-1, -1)Therefore the parallel sides are:
[tex]\sf \overline{HJ} \parallel \overline{LK}\:\: \textsf{ and }\:\: \overline{LK} \parallel \overline{HL}[/tex]
Therefore, the diagonals of the parallelogram are:
[tex]\sf \overline{LJ} \:\: \textsf{ and }\:\:\overline{HK}[/tex]
To find the coordinates of the intersection of the diagonals, either:
draw a diagram (see attached) and determine the point of intersection of the diagonals from the diagram, ordetermine the midpoint of either diagonal (as the diagonals of a parallelogram bisect each other, i.e. divide into 2 equal parts).Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
To find the midpoint of diagonal LJ, define the endpoints:
[tex](x_1,y_1)=L=(-1, -1)[/tex][tex](x_2,y_2)=J=(3,3)[/tex]Substitute the defined endpoints into the formula and solve:
[tex]\begin{aligned} \implies \textsf{Midpoint of LJ} & =\left(\dfrac{3-1}{2},\dfrac{3-1}{2}\right)\\ & =\left(\dfrac{2}{2},\dfrac{2}{2}\right)\\ & =\left(1,1\right) \end{aligned}[/tex]
Therefore, the coordinates off the intersection of the diagonals of parallelogram HJKL are (1, 1).
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Check the order
HJKLMeans H,J and K,L are adjacent coordinates
Hence HK and JL are diagonals
We know diagonals of a parallelogram bisect each other so midpoint of any diagonal would be the intersection point
Midpoint of HK
(x1+x2/2,y1+y2/2)(-1+3/2,4-2/2)(2/2,2/2)(1,1)